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Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments

Author

Listed:
  • Marat Akhmet

    (Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey)

  • Duygu Aruğaslan Çinçin

    (Department of Mathematics, Süleyman Demirel University, Isparta 32260, Turkey)

  • Madina Tleubergenova

    (Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan)

  • Zakhira Nugayeva

    (Department of Mathematics, K. Zhubanov Aktobe Regional University, Aktobe 030000, Kazakhstan
    Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan)

Abstract

This is the first time that the method for the investigation of unpredictable solutions of differential equations has been extended to unpredictable oscillations of neural networks with a generalized piecewise constant argument, which is delayed and advanced. The existence and exponential stability of the unique unpredictable oscillation are proven. According to the theory, the presence of unpredictable oscillations is strong evidence for Poincaré chaos. Consequently, the paper is a contribution to chaos applications in neuroscience. The model is inspired by chaotic time-varying stimuli, which allow studying the distribution of chaotic signals in neural networks. Unpredictable inputs create an excitation wave of neurons that transmit chaotic signals. The technique of analysis includes the ideas used for differential equations with a piecewise constant argument. The results are illustrated by examples and simulations. They are carried out in MATLAB Simulink to demonstrate the simplicity of the diagrammatic approaches.

Suggested Citation

  • Marat Akhmet & Duygu Aruğaslan Çinçin & Madina Tleubergenova & Zakhira Nugayeva, 2021. "Unpredictable Oscillations for Hopfield-Type Neural Networks with Delayed and Advanced Arguments," Mathematics, MDPI, vol. 9(5), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:571-:d:512404
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    References listed on IDEAS

    as
    1. Marat Akhmet & Madina Tleubergenova & Zakhira Nugayeva, 2020. "Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks," Mathematics, MDPI, vol. 8(10), pages 1-14, October.
    2. Huang, Zhenkun & Wang, Xinghua & Xia, Yonghui, 2009. "A topological approach to the existence of solutions for nonlinear differential equations with piecewise constant argument," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1121-1131.
    3. Itamar Daniel Landau & Haim Sompolinsky, 2018. "Coherent chaos in a recurrent neural network with structured connectivity," PLOS Computational Biology, Public Library of Science, vol. 14(12), pages 1-27, December.
    4. Marat Akhmet & Madina Tleubergenova & Mehmet Onur Fen & Zakhira Nugayeva, 2020. "Unpredictable Solutions of Linear Impulsive Systems," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    5. Samuel P Muscinelli & Wulfram Gerstner & Tilo Schwalger, 2019. "How single neuron properties shape chaotic dynamics and signal transmission in random neural networks," PLOS Computational Biology, Public Library of Science, vol. 15(6), pages 1-35, June.
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    Cited by:

    1. Marat Akhmet & Madina Tleubergenova & Akylbek Zhamanshin, 2023. "Compartmental Unpredictable Functions," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    2. Pengfei Guo & Yunong Zhang, 2022. "Tracking Control for Triple-Integrator and Quintuple-Integrator Systems with Single Input Using Zhang Neural Network with Time Delay Caused by Backward Finite-Divided Difference Formulas for Multiple-," Mathematics, MDPI, vol. 10(9), pages 1-27, April.

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